Detecting switches in a volatile environment - Colloque international de la Société des Neurosciences 2019

Should I stay or should I go? Humans adapt to the volatility of visual motion properties, and know about it

Laurent Perrinet, Chloé Pasturel & Anna Montagnini

Colloque international de la Société des Neurosciences 2019, 23/5/2019

Acknowledgements:

Rick Adams and Karl Friston @ UCL - Wellcome Trust Centre for Neuroimaging
Jean-Bernard Damasse and Laurent Madelain - ANR REM
Frédéric Chavane - INT

This work was supported by the PACE-ITN Project.

(AUTHOR) Hello, I am Laurent Perrinet from the Institute of Neurosciences of la Timone in Marseille, a joint unit from the CNRS and the AMU
(OBJECTIVE)
Let's me first describe the motivation of this work...

Today I will present some recent results on detecting switches in a sequence

In particular, I will try to give some principles of active inference, framed in a practical example of a dynamic, poissbly volatile environment and how we may use it to anticipate ---- and my main goal in general is to illustrate how this theory may give a creative and efficient tool to do psychophysics.

https://laurentperrinet.github.io/talk/2016-10-13-law/ https://laurentperrinet.github.io/talk/2018-02-01-bcp-invibe-fest/ https://laurentperrinet.github.io/talk/2018-04-05-bcp-talk/ https://laurentperrinet.github.io/talk/2019-01-18-laconeu/ https://laurentperrinet.github.io/talk/2019-04-05-bbcp-causal-kickoff/

this talk= https://laurentperrinet.github.io/talk/2019-05-23-neurofrance/

(SHOW TITLE)

Motivation: Should I stay or should I go? - Probability bias

Motivation: Should I stay or should I go? - Eye Movements

Montagnini A, Souto D, and Masson GS (2010) J Vis (VSS Abstracts) 10(7):554,
Montagnini A, Perrinet L, and Masson GS (2015) BICV book chapter

Motivation: Should I stay or should I go? - Eye Movements

Motivation: Should I stay or should I go? - Switching model

Outline

Motivation: Should I stay or should I go?

Methods: Experimental protocol

Results:The Bayesian Changepoint Detector

Results: Matching Behavioral data

Results: Analyzing inter-individual differences

Methods: Experimental protocol - Switching model

full code @ github.com/chloepasturel/AnticipatorySPEM

Methods: Experimental protocol - Rating scale

full code @ github.com/chloepasturel/AnticipatorySPEM

First, we overlay the results of the bet result for one of the 12 subjects

We rescaled th value given by the observer so that it fits to 0 (sure it goes left) to 1 (sure it goes right)

We observe a pretty good fit of this trace as a function of trial number

In particular, we see 2 main effects: - results are more variable when the bias is around .5 than when it is high (close to zero or one) - switches were detected quite rapidly but with a certain delay of a few trials. Indeed, note that this plot shows the entire sequence but that observers had only access to some internal representation of the memory of the previous observations. When faced with some new observations, the observer has to constantly adapt his response to either exploit this information by considering that this observation belongs to the same sub-block or to explore a novel hypothesis. This compromise is one of the crucial component that we wish to explore.

Let's now have a look at EMs...

Methods: Experimental protocol - Fitting eye movements

full code @ github.com/chloepasturel/AnticipatorySPEM

I show here a typical velocity traces for one subject / 2 trials

x-axis is time in milliseconds aligned on target onset, and we show respectively from left to right the fixation in gray, the GAP in pink (300ms) and the run in light gray.
y-axis is the velocity as computed as the gradient of position. Remark that the eyelink provides with the periods of saccades or blinks that we removed from the signal. it is quite noisy and to complement existing signal processing methods, Chloe implemented a robust
fitting method which allows to extract some key components of the velocity traces: maximum speed, latency, temporal inertia ($ au$) and most interestingly acceleration before motion onset. We cross-validated that this method was givinfg similar results to other classical methods but in a more robust fashion/

While being sensible to recording errors, this allows us to extract the anticipatory component of SPEMs and..

Methods: Experimental protocol - Fitting eye movements

full code @ github.com/chloepasturel/AnticipatorySPEM

I show here a typical velocity traces for one subject / 2 trials

x-axis is time in milliseconds aligned on target onset, and we show respectively from left to right the fixation in gray, the GAP in pink (300ms) and the run in light gray.
y-axis is the velocity as computed as the gradient of position. Remark that the eyelink provides with the periods of saccades or blinks that we removed from the signal. it is quite noisy and to complement existing signal processing methods, Chloe implemented a robust
fitting method which allows to extract some key components of the velocity traces: maximum speed, latency, temporal inertia ($ au$) and most interestingly acceleration before motion onset. We cross-validated that this method was givinfg similar results to other classical methods but in a more robust fashion/

While being sensible to recording errors, this allows us to extract the anticipatory component of SPEMs and..

Methods: Experimental protocol - Eye Movements

full code @ github.com/chloepasturel/AnticipatorySPEM

Methods: Experimental protocol - Behaviour

full code @ github.com/chloepasturel/AnticipatorySPEM

Methods: Experimental protocol

full code @ github.com/chloepasturel/AnticipatorySPEM

quantitatively, one can now plot the results for all subjects
the x-axis corresponds to the probability that was coded at the second layer and which is unknown to the observer
the y -axis shows either the bet or the
dots represent single responses - the saturation giving the identity of the observer

we notice a quite nice linear correlation (black line) for both experiments; of the order of that found in the classical experiment with fixed blocks and a vartiety of bias values. This is surprising as the blocks are of random length, observer can still adapt to such a volatile environment.

Another visualization, the scatter plot of acceleration as a function of probability bet shows also that there is a correlation between both variables.

This allows to make a first point: it is possible to use more genreal models such as hierarchical generative models.

However, while this results seem encouraging, a more finer analysis may be necessary.

Outline

Motivation: Should I stay or should I go?

Methods: Experimental protocol

Results:The Bayesian Changepoint Detector

Results: Matching Behavioral data

Results: Analyzing inter-individual differences

Results:The Bayesian Changepoint Detector - Switching model

full code @ github.com/chloepasturel/AnticipatorySPEM

Let's remember our hierarchical generative model.

At any given trial, we wish to construct an algorithm which

We will introduce a fundamental component of Bayesian models : a latent variable

this new variable will be used to test different hypothesis which will be evaluated to predict future states. it is called latent because it aims at representing a variable that is latent (or hidden) to the observer

in our case, we will assume that the bayesian model knows about the structure of the generative model and we will set it to the current run-length $r$, that is, at any given trial, the hypothesis that the past r observations belong to the same block. of course a wrong choice of a latent variables (let's say the temperture in the experimental room) may give unexpected results, even is the bayesian model is "optimal" - an essential point to understand in bayesian inference

Results:The Bayesian Changepoint Detector

Initialize $P(r_0=0)=1$ and $ν^{(0)}_1 = ν_{prior}$ and $χ^{(0)}_1 = χ_{prior}$

Results:The Bayesian Changepoint Detector

Observe New Datum $x_t$ and Perform Prediction $P (x_{t+1} | x_{1:t}) = P (x_{t+1}|x_{1:t} , r_t) \cdot P (r_t|x_{1:t})$

Results:The Bayesian Changepoint Detector

Evaluate (likelihood) Predictive Probability $π_{1:t} = P(x_t |ν^{(r)}_t,χ^{(r)}_t)$
Calculate Growth Probabilities $P(r_t=r_{t-1}+1, x_{1:t}) = P(r_{t-1}, x_{1:t-1}) \cdot π^{(r)}_t \cdot (1−h))$
Calculate Changepoint Probabilities $P(r_t=0, x_{1:t})= \sum_{r_{t-1}} P(r_{t-1}, x_{1:t-1}) \cdot π^{(r)}_t \cdot h$

Results:The Bayesian Changepoint Detector

Calculate Evidence $P(x_{1:t}) = \sum_{r_{t-1}} P (r_t, x_{1:t})$
Determine Run Length Distribution $P (r_t | x_{1:t}) = P (r_t, x_{1:t})/P (x_{1:t}) $

Results:The Bayesian Changepoint Detector

Update Sufficient Statistics :
$ν^{(r+1)}_{t+1} = ν^{(r)}_{t} +1$, $χ^{(r+1)}_{t+1} = χ^{(r)}_{t} + u(x_t)$
$ν^{(0)}_{t+1} = ν_{prior}$, $χ^{(0)}_{t+1} = χ_{prior}$

Bayesian Changepoint Detector

Initialize

$P(r_0=0)=1$ and
$ν^{(0)}_1 = ν_{prior}$ and $χ^{(0)}_1 = χ_{prior}$

Observe New Datum $x_t$
Evaluate Predictive Probability $π_{1:t} = P(x_t |ν^{(r)}_t,χ^{(r)}_t)$
Calculate Growth Probabilities $P(r_t=r_{t-1}+1, x_{1:t}) = P(r_{t-1}, x_{1:t-1}) \cdot π^{(r)}_t \cdot (1−H(r^{(r)}_{t-1}))$
Calculate Changepoint Probabilities $P(r_t=0, x_{1:t})= \sum_{r_{t-1}} P(r_{t-1}, x_{1:t-1}) \cdot π^{(r)}_t \cdot H(r^{(r)}_{t-1})$
Calculate Evidence $P(x_{1:t}) = \sum_{r_{t-1}} P (r_t, x_{1:t})$
Determine Run Length Distribution $P (r_t | x_{1:t}) = P (r_t, x_{1:t})/P (x_{1:t}) $
Update Sufficient Statistics :

$ν^{(0)}_{t+1} = ν_{prior}$, $χ^{(0)}_{t+1} = χ_{prior}$
$ν^{(r+1)}_{t+1} = ν^{(r)}_{t} +1$, $χ^{(r+1)}_{t+1} = χ^{(r)}_{t} + u(x_t)$

Perform Prediction $P (x_{t+1} | x_{1:t}) = P (x_{t+1}|x_{1:t} , r_t) \cdot P (r_t|x_{1:t})$
go to (2)

Results:The Bayesian Changepoint Detector

full code @ github.com/laurentperrinet/bayesianchangepoint

Results:The Bayesian Changepoint Detector - Compiling results

Outline

Motivation: Should I stay or should I go?

Methods: Experimental protocol

Results:The Bayesian Changepoint Detector

Results: Matching Behavioral data

Results: Analyzing inter-individual differences

Results: Matching Behavioral data - Compiling results

Results: Matching Behavioral data - fit with BCP

Results: Matching Behavioral data

full code @ github.com/laurentperrinet/bayesianchangepoint

Results: Matching Behavioral data

full code @ github.com/laurentperrinet/bayesianchangepoint

Results: Matching Behavioral data

full code @ github.com/laurentperrinet/bayesianchangepoint

Results: Matching Behavioral data - Fixed window

Results: Matching Behavioral data - Full model

Outline

Motivation: Should I stay or should I go?

Methods: Experimental protocol

Results:The Bayesian Changepoint Detector

Results: Matching Behavioral data

Results: Analyzing inter-individual differences

Results: Analyzing inter-individual differencesinterindividual differences

Should I stay or should I go? Humans adapt to the volatility of visual motion properties, and know about it

Laurent Perrinet, Chloé Pasturel & Anna Montagnini

Colloque international de la Société des Neurosciences 2019, 23/5/2019

Acknowledgements:

Rick Adams and Karl Friston @ UCL - Wellcome Trust Centre for Neuroimaging
Jean-Bernard Damasse and Laurent Madelain - ANR REM
Frédéric Chavane - INT

This work was supported by the PACE-ITN Project.

https://laurentperrinet.github.io/talk/2019-05-23-neurofrance